City failed in their pursuit of the Chile star during the previous transfer window but there is strong speculation they will attempt to strike a deal next month, with Sanchez's contract expiring at the end of the season.
Gabriel Jesus picked up an injury in the 0-0 draw with Crystal Palace on Sunday that manager Pep Guardiola says could keep him out for up to two months, encouraging talk of an imminent City bid for Sanchez
Guardiola himself stated he expects the 29-year-old to stay at the Emirates Stadium, though, and Wenger was in no mood to discuss the issue further after his side were held to a 1-1 draw at West Brom courtesy of Jay Rodriguez's controversial late penalty.
Asked if Sanchez had played his last game for Arsenal at The Hawthorns, Wenger told a news conference: "We play on Wednesday [against Chelsea].
"I have spoken many times about that. I'm not ready to talk about that some more.
"I have given you my answer many times. I don't see why I should come back to a subject we have talked about 155 times."
Premier League (@premierleague) December 31, 2017
Wenger also hit back at club legend Thierry Henry after his suggestion that Arsenal players' mixed celebrations during the 3-1 win at Crystal Palace this week pointed to a dressing-room rift caused by Sanchez's uncertain future.
"It was never a problem inside [the club]," he said. "I don't listen to what he says and other people says.
"We focus on our own problems, that's the only thing.
"There are people who are paid to talk. It's difficult sometimes when you are paid to talk, to talk, to talk and only say things that are true and intelligent."
Asked if Arsenal will look to make signings in the transfer window, Wenger added: "Tomorrow [Monday], I will try to bring myself in first and, after that, we will see."